結果
| 問題 | No.1361 [Zelkova 4th Tune *] QUADRUPLE-SEQUENCEの詩 |
| コンテスト | |
| ユーザー |
 hos.lyric
|
| 提出日時 | 2021-01-22 21:51:37 |
| 言語 | D (dmd 2.109.1) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 10,242 bytes |
| 記録 | |
| コンパイル時間 | 1,955 ms |
| コンパイル使用メモリ | 170,748 KB |
| 実行使用メモリ | 18,020 KB |
| 最終ジャッジ日時 | 2024-06-22 10:41:34 |
| 合計ジャッジ時間 | 7,357 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 9 RE * 9 TLE * 1 -- * 55 |
ソースコード
import std.conv, std.functional, std.range, std.stdio, std.string;
import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons;
import core.bitop;
class EOFException : Throwable { this() { super("EOF"); } }
string[] tokens;
string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; }
int readInt() { return readToken.to!int; }
long readLong() { return readToken.to!long; }
real readReal() { return readToken.to!real; }
bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } }
bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } }
int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; }
int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); }
int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); }
// a^-1 (mod m)
long modInv(long a, long m)
in {
assert(m > 0, "modInv: m > 0 must hold");
}
do {
long b = m, x = 1, y = 0, t;
for (; ; ) {
t = a / b; a -= t * b;
if (a == 0) {
assert(b == 1 || b == -1, "modInv: gcd(a, m) != 1");
if (b == -1) y = -y;
return (y < 0) ? (y + m) : y;
}
x -= t * y;
t = b / a; b -= t * a;
if (b == 0) {
assert(a == 1 || a == -1, "modInv: gcd(a, m) != 1");
if (a == -1) x = -x;
return (x < 0) ? (x + m) : x;
}
y -= t * x;
}
}
// M: prime, G: primitive root
class Fft(int M_, int G, int K) {
import std.algorithm : reverse;
import std.traits : isIntegral;
alias M = M_;
// 1, 1/4, 1/8, 3/8, 1/16, 5/16, 3/16, 7/16, ...
int[] gs;
this() {
static assert(2 <= K && K <= 30, "Fft: 2 <= K <= 30 must hold");
static assert(!((M - 1) & ((1 << K) - 1)), "Fft: 2^K | M - 1 must hold");
gs = new int[1 << (K - 1)];
gs[0] = 1;
long g2 = G, gg = 1;
for (int e = (M - 1) >> K; e; e >>= 1) {
if (e & 1) gg = (gg * g2) % M;
g2 = (g2 * g2) % M;
}
gs[1 << (K - 2)] = cast(int)(gg);
for (int l = 1 << (K - 2); l >= 2; l >>= 1) {
gs[l >> 1] = cast(int)((cast(long)(gs[l]) * gs[l]) % M);
}
assert((cast(long)(gs[1]) * gs[1]) % M == M - 1,
"Fft: g^(2^(K-1)) == -1 (mod M) must hold");
for (int l = 2; l <= 1 << (K - 2); l <<= 1) {
foreach (i; 1 .. l) {
gs[l + i] = cast(int)((cast(long)(gs[l]) * gs[i]) % M);
}
}
}
void fft(int[] xs) const {
const n = cast(int)(xs.length);
assert(!(n & (n - 1)), "Fft.fft: |xs| must be a power of two");
assert(n <= 1 << K, "Fft.fft: |xs| <= 2^K must hold");
for (int l = n; l >>= 1; ) {
foreach (i; 0 .. (n >> 1) / l) {
const(long) g = gs[i];
foreach (j; (i << 1) * l .. (i << 1 | 1) * l) {
const t = cast(int)((g * xs[j + l]) % M);
if ((xs[j + l] = xs[j] - t) < 0) xs[j + l] += M;
if ((xs[j] += t) >= M) xs[j] -= M;
}
}
}
}
void invFft(int[] xs) const {
const n = cast(int)(xs.length);
assert(!(n & (n - 1)), "Fft.invFft: |xs| must be a power of two");
assert(n <= 1 << K, "Fft.invFft: |xs| <= 2^K must hold");
for (int l = 1; l < n; l <<= 1) reverse(xs[l .. l << 1]);
for (int l = 1; l < n; l <<= 1) {
foreach (i; 0 .. (n >> 1) / l) {
const(long) g = gs[i];
foreach (j; (i << 1) * l .. (i << 1 | 1) * l) {
int t = cast(int)((g * (xs[j] - xs[j + l])) % M);
if (t < 0) t += M;
if ((xs[j] += xs[j + l]) >= M) xs[j] -= M;
xs[j + l] = t;
}
}
}
}
T[] convolute(T)(inout(T)[] as, inout(T)[] bs) const if (isIntegral!T) {
const na = cast(int)(as.length), nb = cast(int)(bs.length);
int n, invN = 1;
for (n = 1; n < na + nb - 1; n <<= 1) {
invN = ((invN & 1) ? (invN + M) : invN) >> 1;
}
auto xs = new int[n], ys = new int[n];
foreach (i; 0 .. na) if ((xs[i] = cast(int)(as[i] % M)) < 0) xs[i] += M;
foreach (i; 0 .. nb) if ((ys[i] = cast(int)(bs[i] % M)) < 0) ys[i] += M;
fft(xs);
fft(ys);
foreach (i; 0 .. n) {
xs[i] = cast(int)((((cast(long)(xs[i]) * ys[i]) % M) * invN) % M);
}
invFft(xs);
auto cs = new T[na + nb - 1];
foreach (i; 0 .. na + nb - 1) cs[i] = cast(T)(xs[i]);
return cs;
}
/*
ModInt!M[] convolute(inout(ModInt!M)[] as, inout(ModInt!M)[] bs) const {
const na = cast(int)(as.length), nb = cast(int)(bs.length);
int n, invN = 1;
for (n = 1; n < na + nb - 1; n <<= 1) {
invN = ((invN & 1) ? (invN + M) : invN) >> 1;
}
auto xs = new int[n], ys = new int[n];
foreach (i; 0 .. na) xs[i] = as[i].x;
foreach (i; 0 .. nb) ys[i] = bs[i].x;
fft(xs);
fft(ys);
foreach (i; 0 .. n) {
xs[i] = cast(int)((((cast(long)(xs[i]) * ys[i]) % M) * invN) % M);
}
invFft(xs);
auto cs = new ModInt!M[na + nb - 1];
foreach (i; 0 .. na + nb - 1) cs[i].x = xs[i];
return cs;
}
int[] convolute(int M1)(inout(ModInt!M1)[] as, inout(ModInt!M1)[] bs) const
if (M != M1) {
const na = cast(int)(as.length), nb = cast(int)(bs.length);
int n, invN = 1;
for (n = 1; n < na + nb - 1; n <<= 1) {
invN = ((invN & 1) ? (invN + M) : invN) >> 1;
}
auto xs = new int[n], ys = new int[n];
foreach (i; 0 .. na) xs[i] = as[i].x;
foreach (i; 0 .. nb) ys[i] = bs[i].x;
fft(xs);
fft(ys);
foreach (i; 0 .. n) {
xs[i] = cast(int)((((cast(long)(xs[i]) * ys[i]) % M) * invN) % M);
}
invFft(xs);
return xs[0 .. na + nb - 1];
}
*/
}
alias Fft0 = Fft!(998244353, 3, 20);
// Fft3_0.M Fft3_1.M Fft3_2.M > 1.15 * 10^27, > 2^89.9
//*
enum FFT_K = 20;
alias Fft3_0 = Fft!(1045430273, 3, FFT_K); // 2^20 997 + 1
alias Fft3_1 = Fft!(1051721729, 6, FFT_K); // 2^20 1003 + 1
alias Fft3_2 = Fft!(1053818881, 7, FFT_K); // 2^20 1005 + 1
//*/
// Fft3_0.M Fft3_1.M Fft3_2.M > 5.95 * 10^25, > 2^85.6
/*
enum FFT_K = 24;
alias Fft3_0 = Fft!(167772161, 3, FFT_K); // 2^25 5 + 1
alias Fft3_1 = Fft!(469762049, 3, FFT_K); // 2^26 7 + 1
alias Fft3_2 = Fft!(754974721, 11, FFT_K); // 2^24 45 + 1
//*/
enum long FFT_INV01 = modInv(Fft3_0.M, Fft3_1.M);
enum long FFT_INV012 = modInv(cast(long)(Fft3_0.M) * Fft3_1.M, Fft3_2.M);
Fft3_0 FFT3_0;
Fft3_1 FFT3_1;
Fft3_2 FFT3_2;
void initFft3() {
FFT3_0 = new Fft3_0;
FFT3_1 = new Fft3_1;
FFT3_2 = new Fft3_2;
}
// for negative result, if (!(0 <= c && c < <bound>)) add MMM:
// enum MMM = 1L * Fft3_0.M * Fft3_1.M * Fft3_2.M;
long[] convolute(inout(long)[] as, inout(long)[] bs) {
const cs0 = FFT3_0.convolute(as, bs);
const cs1 = FFT3_1.convolute(as, bs);
const cs2 = FFT3_2.convolute(as, bs);
auto cs = new long[cs0.length];
foreach (i; 0 .. cs0.length) {
long d0 = cs0[i] % Fft3_0.M;
long d1 = (FFT_INV01 * (cs1[i] - d0)) % Fft3_1.M;
if (d1 < 0) d1 += Fft3_1.M;
long d2 =
(FFT_INV012 * ((cs2[i] - d0 - Fft3_0.M * d1) % Fft3_2.M)) % Fft3_2.M;
if (d2 < 0) d2 += Fft3_2.M;
cs[i] = d0 + Fft3_0.M * d1 + (cast(long)(Fft3_0.M) * Fft3_1.M) * d2;
}
return cs;
}
void main() {
initFft3;
try {
for (; ; ) {
auto N = new int[4];
foreach (h; 0 .. 4) {
N[h] = readInt();
}
const S = readLong();
auto A = new long[][4];
foreach (h; 0 .. 4) {
A[h] = new long[N[h]];
foreach (i; 0 .. N[h]) {
A[h][i] = readLong();
}
}
alias Entry = Tuple!(long, "val", int, "i", int, "j");
Entry[] fs, gs;
foreach (i; 0 .. N[0]) foreach (j; 0 .. N[1]) {
fs ~= Entry(A[0][i] * A[1][j], i, j);
}
foreach (i; 0 .. N[2]) foreach (j; 0 .. N[3]) {
gs ~= Entry(A[2][i] * A[3][j], i, j);
}
fs.sort;
gs.sort;
const fsLen = cast(int)(fs.length);
const gsLen = cast(int)(gs.length);
const int lbF = fs.lowerBound(Entry(0, int.min, int.min));
const int ubF = fs.upperBound(Entry(0, int.max, int.max));
const int lbG = gs.lowerBound(Entry(0, int.min, int.min));
const int ubG = gs.upperBound(Entry(0, int.max, int.max));
// <= t
long calc(long t) {
long ret;
if (0 <= t) {
ret += 1L * (ubF - lbF) * (gsLen - 0);
ret += 1L * (fsLen - 0) * (ubG - lbG);
ret -= 1L * (ubF - lbF) * (ubG - lbG);
ret += 1L * (lbF - 0) * (gsLen - ubG);
ret += 1L * (fsLen - ubF) * (lbG - 0);
for (int i = lbF, j = 0; j < lbG; ++j) {
for (; i > 0 && fs[i - 1].val * gs[j].val <= t; --i) {}
ret += (lbF - i);
}
for (int i = ubF, j = gsLen; --j >= ubG; ) {
for (; i < fsLen && fs[i].val * gs[j].val <= t; ++i) {}
ret += (i - ubF);
}
} else {
for (int i = 0, j = ubG; j < gsLen; ++j) {
for (; i < lbF && fs[i].val * gs[j].val <= t; ++t) {}
ret += (i - 0);
}
for (int i = fsLen, j = lbG; --j >= 0; ) {
for (; i > ubF && fs[i - 1].val * gs[j - 1].val <= t; --i) {}
ret += (fsLen - i);
}
}
return ret;
}
long lo = -10L^^18, hi = +10L^^18;
for (; lo + 1 < hi; ) {
const mid = (lo + hi) / 2;
((calc(mid) >= S) ? hi : lo) = mid;
}
writeln(hi);
if (hi == 0) {
writefln("%s %s %s %s",
A[0][fs[lbF].i], A[1][fs[lbF].j],
A[2][gs[lbG].i], A[3][gs[lbG].j]);
} else {
foreach (ref g; gs) {
if (g.val != 0 && hi % g.val == 0) {
const tar = hi / g.val;
const pos = fs.lowerBound(Entry(tar, int.min, int.min));
if (pos < fsLen && fs[pos].val == tar) {
writefln("%s %s %s %s",
A[0][fs[pos].i], A[1][fs[pos].j],
A[2][g.i], A[3][g.j]);
break;
}
}
}
}
}
} catch (EOFException e) {
}
}